# Properties

 Label 1296.3 Level 1296 Weight 3 Dimension 41220 Nonzero newspaces 16 Sturm bound 279936 Trace bound 7

## Defining parameters

 Level: $$N$$ = $$1296 = 2^{4} \cdot 3^{4}$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$16$$ Sturm bound: $$279936$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(1296))$$.

Total New Old
Modular forms 94824 41724 53100
Cusp forms 91800 41220 50580
Eisenstein series 3024 504 2520

## Trace form

 $$41220 q - 48 q^{2} - 54 q^{3} - 80 q^{4} - 60 q^{5} - 72 q^{6} - 60 q^{7} - 48 q^{8} - 18 q^{9} + O(q^{10})$$ $$41220 q - 48 q^{2} - 54 q^{3} - 80 q^{4} - 60 q^{5} - 72 q^{6} - 60 q^{7} - 48 q^{8} - 18 q^{9} - 116 q^{10} - 36 q^{11} - 72 q^{12} - 100 q^{13} - 48 q^{14} - 54 q^{15} - 80 q^{16} - 105 q^{17} - 72 q^{18} - 87 q^{19} - 48 q^{20} - 90 q^{21} - 80 q^{22} - 36 q^{23} - 72 q^{24} + 5 q^{25} - 48 q^{26} - 54 q^{27} - 116 q^{28} + 84 q^{29} - 72 q^{30} + 12 q^{31} - 48 q^{32} - 162 q^{33} - 80 q^{34} - 39 q^{35} - 72 q^{36} - 193 q^{37} - 48 q^{38} - 54 q^{39} - 80 q^{40} - 156 q^{41} - 72 q^{42} - 204 q^{43} - 48 q^{44} - 90 q^{45} - 148 q^{46} - 252 q^{47} - 72 q^{48} - 229 q^{49} - 48 q^{50} - 54 q^{51} - 80 q^{52} - 75 q^{53} - 72 q^{54} - 137 q^{55} - 636 q^{56} - 18 q^{57} - 704 q^{58} - 252 q^{59} - 72 q^{60} - 580 q^{61} - 1236 q^{62} - 54 q^{63} - 620 q^{64} - 684 q^{65} - 72 q^{66} - 156 q^{67} - 516 q^{68} - 90 q^{69} - 224 q^{70} - 51 q^{71} - 72 q^{72} + 67 q^{73} + 456 q^{74} - 54 q^{75} + 640 q^{76} + 516 q^{77} - 72 q^{78} + 132 q^{79} + 1572 q^{80} - 162 q^{81} + 568 q^{82} + 324 q^{83} - 72 q^{84} + 397 q^{85} + 1752 q^{86} - 54 q^{87} + 736 q^{88} - 657 q^{89} - 72 q^{90} - 1141 q^{91} - 48 q^{92} - 1602 q^{93} - 48 q^{94} - 3201 q^{95} - 72 q^{96} - 1020 q^{97} - 48 q^{98} - 1350 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(1296))$$

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
1296.3.b $$\chi_{1296}(487, \cdot)$$ None 0 1
1296.3.e $$\chi_{1296}(161, \cdot)$$ 1296.3.e.a 2 1
1296.3.e.b 4
1296.3.e.c 4
1296.3.e.d 4
1296.3.e.e 4
1296.3.e.f 4
1296.3.e.g 4
1296.3.e.h 4
1296.3.e.i 8
1296.3.e.j 8
1296.3.g $$\chi_{1296}(1135, \cdot)$$ 1296.3.g.a 2 1
1296.3.g.b 2
1296.3.g.c 4
1296.3.g.d 4
1296.3.g.e 4
1296.3.g.f 4
1296.3.g.g 4
1296.3.g.h 4
1296.3.g.i 4
1296.3.g.j 8
1296.3.g.k 8
1296.3.h $$\chi_{1296}(809, \cdot)$$ None 0 1
1296.3.j $$\chi_{1296}(485, \cdot)$$ n/a 376 2
1296.3.m $$\chi_{1296}(163, \cdot)$$ n/a 376 2
1296.3.n $$\chi_{1296}(377, \cdot)$$ None 0 2
1296.3.o $$\chi_{1296}(271, \cdot)$$ 1296.3.o.a 2 2
1296.3.o.b 2
1296.3.o.c 2
1296.3.o.d 2
1296.3.o.e 2
1296.3.o.f 2
1296.3.o.g 2
1296.3.o.h 2
1296.3.o.i 2
1296.3.o.j 2
1296.3.o.k 2
1296.3.o.l 2
1296.3.o.m 2
1296.3.o.n 2
1296.3.o.o 2
1296.3.o.p 2
1296.3.o.q 4
1296.3.o.r 4
1296.3.o.s 4
1296.3.o.t 4
1296.3.o.u 4
1296.3.o.v 4
1296.3.o.w 4
1296.3.o.x 4
1296.3.o.y 4
1296.3.o.z 4
1296.3.o.ba 4
1296.3.o.bb 4
1296.3.o.bc 4
1296.3.o.bd 4
1296.3.o.be 4
1296.3.o.bf 4
1296.3.q $$\chi_{1296}(593, \cdot)$$ 1296.3.q.a 2 2
1296.3.q.b 2
1296.3.q.c 2
1296.3.q.d 4
1296.3.q.e 4
1296.3.q.f 4
1296.3.q.g 4
1296.3.q.h 4
1296.3.q.i 4
1296.3.q.j 4
1296.3.q.k 4
1296.3.q.l 8
1296.3.q.m 8
1296.3.q.n 8
1296.3.q.o 8
1296.3.q.p 8
1296.3.q.q 16
1296.3.t $$\chi_{1296}(55, \cdot)$$ None 0 2
1296.3.w $$\chi_{1296}(379, \cdot)$$ n/a 760 4
1296.3.x $$\chi_{1296}(53, \cdot)$$ n/a 760 4
1296.3.z $$\chi_{1296}(199, \cdot)$$ None 0 6
1296.3.ba $$\chi_{1296}(127, \cdot)$$ n/a 216 6
1296.3.bc $$\chi_{1296}(17, \cdot)$$ n/a 210 6
1296.3.bf $$\chi_{1296}(89, \cdot)$$ None 0 6
1296.3.bi $$\chi_{1296}(19, \cdot)$$ n/a 1704 12
1296.3.bj $$\chi_{1296}(125, \cdot)$$ n/a 1704 12
1296.3.bl $$\chi_{1296}(41, \cdot)$$ None 0 18
1296.3.bm $$\chi_{1296}(31, \cdot)$$ n/a 1944 18
1296.3.bo $$\chi_{1296}(65, \cdot)$$ n/a 1926 18
1296.3.br $$\chi_{1296}(7, \cdot)$$ None 0 18
1296.3.bt $$\chi_{1296}(43, \cdot)$$ n/a 15480 36
1296.3.bu $$\chi_{1296}(5, \cdot)$$ n/a 15480 36

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(1296))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(1296)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 10}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 15}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 10}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 9}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(81))$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(108))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(162))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(216))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(324))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(432))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(648))$$$$^{\oplus 2}$$